A Chemical-Pressure-Induced Phase Transition Controlled by Lone Electron Pair Activity

The chemical pressure approach offers a new paradigm for property control in functional materials. In this work, we disclose a correlation between the β → α pressure-induced phase transition in SnMoO4 and the substitution process of Mo6+ by W6+ in SnMo1–xWxO4 solid solutions (x = 0–1). Special attention is paid to discriminating the role of the lone pair Sn2+ cation from the structural distortive effect along the Mo/W substitution process, which is crucial to disentangle the driven force of the transition phase. Furthermore, the reverse α → β transition observed at high temperature in SnWO4 is rationalized on the same basis as a negative pressure effect associated with a decreasing of W6+ percentage in the solid solution. This work opens a versatile chemical approach in which the types of interactions along the formation of solid solutions are clearly differentiated and can also be used to tune their properties, providing opportunities for the development of new materials.


1.-Computational details a) General Aspects
The structural, electronic properties and EOS of crystalline SnMoO4 and SnWO4 pure compounds were evaluated under the periodic DFT framework using the CRYSTAL17 package. 1,2 To study the influence of different approximations for exchange and correlation contributions to the DFT energy, a complete structure optimization by using the HSE06 3,4 and B3LYP 5 functionals has been performed.
The atoms were described using pseudopotential basis sets: tungsten was described by a large-core ECP, derived by Hay and Wadt and modified by Cora et al., 6 molybdenum by Mo-976-311 (d631)G, 7 tin by Sn_ECP28MDF-411(51d) G, 8 and oxygen by O_6-31d1G (all-electron). 9 The accuracy of the evaluation of the Coulomb and exchange series was controlled by five thresholds, whose adopted values were 10 −7 (overlap threshold for Coulomb integrals), 10 −7 (penetration threshold for Coulomb integrals), 10 −7 (overlap threshold for HF exchange integrals), 10 −7 and 10 −14 (pseudo-overlap for HF exchange series), which assure a convergence in total energy better than 10 -7 Hartree in all cases. The percent of Fock/Kohn-Sham matrices mixing has been set to 40 (IPMIX= 40).
The CRYSTAL program can perform an automatic scan over the volume to compute energy E versus volume V data that are then described by the third-order Birch−Murnaghan (BM-3) EOS. 10,11 For each volume, a full V-constrained geometry optimization was performed. As a result, the pressure dependence of the unit cell structure was determined, as well as the volume/pressure dependence of the total energy and enthalpy. In addition, an automatic scheme for computing the quasi-harmonic approximation (QHA) crystal properties has been used, considering a volume range extending from a − 3% compression to a + 6% expansion around the equilibrium unit cell volume. The band structures and projected densities of states (DOS) on atoms and orbitals were performed to analyze the electronic structure.
Electron Localization Function (ELF) and Crystal Orbital Hamilton Population (COHP) analysis were obtained from single point calculations using VASP 12,13 at the optimized unit cell obtained from HSE06 CRYSTAL calculations. In this VASP calculations, we used the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional 14 and k-point gamma-centered Monkhorst-Pack meshes with a reciprocal spacing of 2π x 0.1 Å -1 . A kinetic energy cutoff of 600 eV for the plane wave basis set expansion was used to solve Kohn−Sham equations. The pseudopotentials utilized for Mo, W Sn and O atoms were standard projector-augmented wave pseudopotentials 15 provided in VASP code. The valence electrons considered for each atomic species are Mo (4s² 4p⁶ 4d 5 5s 1 ), W (5s 2 5p 6 5d 4 6s 2 ), Sn (4d¹⁰5s 2 5p²) and O (2s 2 2s 4 ). COHP and the negative of the COHP integrated to the Fermi level were calculated by using the LOBSTER package. 16,17 . PbeVaspFit2015 atomic basis were used to project the plane waves as implemented in the LOBSTER code. Specifically, the following atomic orbitals for each atomic species were used: O 2s 2p, Sn 4d 4p 4s 5p 5s, W 5d 5p 5s 6s and Mo 4d 4p 4s 5s.

b) Solid Solutions
In both structures (α and β), the number of formula units is Z=4. If one, two or three of the Mo positions are replaced by one, two or three W atoms, a 25%, 50% or 75% of substitution will be obtained. In the case of a 50% replacement, there are 3 different possibilities concerning the relative positions of the Mo and W atoms in the unit cell. We have computed all of them and selected the most energetically favorable.